To find the initial amount of the investment, we need to understand how the investment grows over time. The investment increases 1.5 times every 7 years.
First, we determine how many 7-year periods are there in 21 years:
\[ \text{Number of periods} = \frac{21 \text{ years}}{7 \text{ years/period}} = 3 \text{ periods} \]
Now, after 3 periods, the value of the investment will be:
\[ \text{Final Value} = \text{Initial Amount} \times (1.5)^3 \]
We know the final value is $16,875, so we can set up the equation:
\[ 16,875 = \text{Initial Amount} \times (1.5)^3 \]
Calculating \( (1.5)^3 \):
\[ (1.5)^3 = 1.5 \times 1.5 \times 1.5 = 2.25 \times 1.5 = 3.375 \]
Now substituting this back in:
\[ 16,875 = \text{Initial Amount} \times 3.375 \]
To find the initial amount, we divide both sides by 3.375:
\[ \text{Initial Amount} = \frac{16,875}{3.375} \]
Calculating this gives:
\[ \text{Initial Amount} = 5000 \]
Thus, the initial amount of the investment was $5,000.
The answer is \( \boxed{5000} \).
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